By using the different relation a=1/sqrt(1+z) instead of a=1/(1+z) there are many advantages
- matter density appears to be 0.25 from late universe experiments
- matter density appears to be 0.333 from supernovae
- matter density really 1.0 and there is no need for dark energy
- no coincidence problem
- an explanation of the Hubble tension
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The scale-factor relation does not appear to change over distance, except that values obtained from galaxies within a few hundred million light-years of us are larger than those obtained from galaxies much farther away. But there is a strong suggestion that we lie in a sort of super-void, and the gravity of galaxies at the edge of the super-void is pulling galaxies near us away from us at a few km/sec/Mpc faster than the value for the Universe as a whole. So it is quite possible that, as predicted by Einstein, the value at any given time is exactly the same no matter where you are in the Universe. It does change with time, because as the Universe expands the gravity of its mass is losing the battle with the intrinsic acceleration of the increasingly large amounts of empty space. Odds are that the current value of 67 to 73 km/sec/Mpc (I use 70 for both historical reasons and as an average of the two current values) will asymptotically (that means slowly at first, then slower and slower, until it stops increasing) to somewhere in the range of 80 or so km/sec (since the mass of the Universe is already only 23% or so of the mass needed to stop the acceleration, the expansion speed can't be very far from its maximum value).
Yes, it's possible that we live in a super-void, but the suggestion in the discussion is that a more fundamental and radical change to our assumptions is needed. It seems to be necessary and is giving good results...
Yes, as a radial inhomogeneity can resemble an (apparent) acceleration, redshift/scale-factor relationship could be explained by modified gravity.
https://iopscience.iop.org/article/10.1088/1361-6382/aceacc
Thus, dark energy and dark matter could be unnecessary (fictitious) magnitudes.
The redshift scale factor relation is not a free function in GR. It is determined from the FLRW metric by computing the path integral along the photon's trajectory.
To change the redshift scale factor relation, one would first have to change the FLRW metric such that the scale factor a(t) was raised to a different power. Thus a(t) ---> f(a(t)) where f is some function of a. But this appears to be quibbling, since then f becomes the effective physical scale factor, and we are right back where we started.
To implement such a theory would therefore require an additional degree of freedom, such as a new medium beyond the vacuum, or an additional field beyond that of gravity. Perhaps one could resurrect tired light.
Thankyou Kathleen, perhaps there is some mistake in the way we are computing things from the FLRW metric. Failing to take quantum effects into account for example. If we derive redshift from the conservation of energy of the photon via h0f0 =h1f1 and h=h0exp(2Ht) where H is the expansion parameter, half of the Hubble parameter, then we get a good match to observations without any need for dark energy. Experiments would measure the matter density to be (1/2)^2=0.25 or 1/3 from low redshift supernovae, as is observed. It seems simpler than trying to modify LCDM in many ways.